Lesson 2: Familiarity with terms and notions of augmentation
Before the actual construction class, students need to become familiar with the new vocabulary and concepts. I like to distribute my Platonic models and ask students to identify the following;
1. The name of the model
2. The shape of the faces in the model.
3. The number of faces in the model
4. The number of vertices in the model
5. The number of edges in the model
*** Euler’s formula makes an interesting insert here ***
vertices + faces - edges = 2
This counting encourages students to explain to their classmates how they considered the model as they counted the number of edges, for instance, on an icosahedron. They also have the opportunity to use the terms and become familiar with their meanings.
By now students are familiar with the five Platonic solids and understand the meaning of regular figures. It is time to introduce semi-regular figures. Semi-regular polyhedra are those that have regular faces but also contain more than one kind of regular polygon. There are several types of semi-regular figures … 13 in all.
Truncation: Getting students to understand truncation is not difficult if you have a model of a tetrahedron and a model of a truncated tetrahedron or a cube and a truncated cube.
 
Truncating Platonic solids produce 5 new figures. Each of the 5 Platonic solids can be truncated. There are 8 other semi-regular convex polygons that are created by slicing sides and vertices again. But there are only 13 possible semi-regular polyhedrons. This is a very deep investigation but an option for a motivated student.
Combining two or more polyhedra that appear to intersect each other can create more polyhedra. These are called Compounded polyhedra. Again, show models.
 
intersection of an octahedron and a cube two intersecting tetrahedra
five intersecting tetrahedra
The next important concept is the augmentation of the Platonic solids by
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